Natural selection drives evolving populations up the fitness landscape, the projection from nucleotide sequence space to organismal reproductive success. While it has long been appreciated that topographic complexities on fitness landscapes can arise only as a consequence of epistatic interactions between mutations, evolutionary genetics has mainly focused on epistasis between pairs of mutations. Here we propose a generalization to the classical population genetic treatment of pairwise epistasis that yields expressions for epistasis among arbitrary subsets of mutations of all orders (pairwise, three-way, etc.). Our approach reveals substantial higher-order epistasis in almost every published fitness landscape. Furthermore we demonstrate that higher-order epistasis is critically important in two systems we know best. We conclude that higher-order epistasis deserves empirical and theoretical attention from evolutionary geneticists.

The effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We conclude by highlighting opportunities for further theoretical and experimental work dissecting the influence that epistasis of all orders has on fitness landscape topography and on the efficiency of evolution by natural selection.Electronic supplementary materialThe online version of this article (10.1007/s10955-018-1975-3) contains supplementary material, which is available to authorized users.

The effect of a mutation on the organism often depends on what other mutations are already present in its genome. Geneticists refer to such mutational interactions as epistasis. Pairwise epistatic effects have been recognized for over a century, and their evolutionary implications have received theoretical attention for nearly as long. However, pairwise epistatic interactions themselves can vary with genomic background. This is called higher-order epistasis, and its consequences for evolution are much less well understood. Here, we assess the influence that higher-order epistasis has on the topography of 16 published, biological fitness landscapes. We find that on average, their effects on fitness landscape declines with order, and suggest that notable exceptions to this trend may deserve experimental scrutiny. We explore whether natural selection may have contributed to this finding, and conclude by highlight opportunities for further work dissecting the influence that epistasis of all orders has on the efficiency of natural selection.